Non-Newtonian fluids are liquids that exhibit viscosities that vary with changing shear stress or shear rate. Non-Newtonian fluids may comprise polymers, polymer solutions, emulsions, multiphase fluid mixtures, and the like. These non-Newtonian fluids may be useful as pharmaceuticals, adhesives, food products, personal care products, coating compositions, and the like. A problem with treating non-Newtonian fluids in microchannels relates to the fact that when the non-Newtonian fluids flow at high flow rates, high velocity gradients at the walls of the microchannels are created. This leads to high apparent viscosities and high pressure drops within the microchannels. This invention, in at least one embodiment, provides a solution to this problem.